Subjects/Calculus II/Fundamental Theorem of Calculus/Formula3.3. Fundamental Theorem of CalculusFormulaIn 3.3. Fundamental Theorem of CalculusFormulaCopy LaTeXG′(x)=f(x).VariablesxVariable independiente (variable de integración)fFunción integrandoRelated formulasRelatedFormulaG(x)=∫axf(t)dt,Open formulaOpen in sectionRelatedMore generally, by the chain rule:dxd∫ag(x)f(t)dt=f(g(x))g′(x).Open formulaOpen in sectionRelatedWith both limits variable:dxd∫u(x)v(x)f(t)dt=f(v(x))v′(x)−f(u(x))u′(x).Open formulaOpen in sectionRelatedFormula∫abf(x)dx=F(b)−F(a).Open formulaOpen in section